Vector quantization (VQ) is a data encoding method in which a sample vector consisting of several samples is approximated by the "nearest" vector of a collection of vectors called a code book. Instead of representing the sample vector by its components, it is represented by the code book index of this "nearest" code book vector. This index is transmitted to a decoder, which uses the index to retrieve the corresponding code book vector from a copy of the code book. Vector quantization is used in, for example, speech coding in mobile telephony.
A common distance or distortion measure (see citation, [1]) to determine the "nearest" code book vector is the squared Euclidean distance between sample vector and code book vector.
Another proposed, more complex distance or distortion measure (see citation [2]) is the perceptually weighted squared Euclidean distance, in which errors in low-energy frequency bands are over-weighted while errors in high-energy bands are under-weighted. The effect is that errors in high-energy parts of a signal tend to be allowed (since the high energy will mask them anyway), while errors in low-energy parts tend to be disallowed (since the error energy would otherwise be a significant part of the total signal energy). The weighting may be performed by a weighting filter, the spectral characteristics of which are essentially the inverse of the spectral characteristics of the signal to be encoded. Since the signal characteristics may be time-varying, the weighting filter may also be time-varying (see citation [2]).
A drawback of these methods is that the transmitted index may, due to the influence of the transmission channel, not always be the same as the received index. In these cases, the actually decoded vector may differ significantly from the original sample vector. The weighted squared Euclidean distance has the further drawback that the weighting filter is sometimes determined in a feedback loop, which implies that a received error may influence the weighting filter and therefore the decoded signal for a long time.
An often used approach to reduce the sensitivity to channel errors is to apply forward error correction coding (FEC). In this way the decoder may detect and even correct errors that occurred during transmission before code book lookup. However, a drawback of this method is that redundancy has to be introduced in the code words that are transmitted over the channel. Furthermore, this method requires very long codes in order to give an acceptable error rate performance. A common way to obtain such long code words is to collect indices from several vector quantized sample vectors before the FEC coding is performed. This collecting process results in a substantial delay, which is in general undesirable in real time applications, such as mobile telephony, video and audio transmission.
An alternative approach to error protection is channel optimized vector quantization (COVQ) (see citation. [3]). Instead of protecting the transmitted index against channel errors, COVQ takes into account the statistical properties of the channel already in the code book construction. The idea behind COVQ is that although the wrong code book index may have been received, the decoded code book vector should still be "close" to the original sample vector. A characteristic feature of COVQ is that the number of indices that may be transmitted often is actually smaller than the number of indices that may be received. In this way, the receiver code book may contain vectors "in between" sample vectors corresponding to actually transmitted indices. A channel error may therefore still result in a decoded vector that is "close" to the intended vector. Thus, COVQ offers a jointly optimized vector quantization and channel protection system. Since long code words are not required, the extra delay introduced by FEC coding may be avoided. However, a drawback of COVQ is that it is very computationally intense. Therefore distance and distortion measures have been based on the simple squared Euclidean distance and not on the more complex but preferable perceptually weighted distance measure.